SOLUTION: Find the sum of n terms of the series 6 + 66 + 666 + . . . .

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Question 1204834: Find the sum of
n
terms of the series
6
+
66
+
666
+
.
.
.
.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
6 +66+666+.....
This is neither an AP OR a GP
6(1+11+111....)
multiply and divide by 9

=6/9( 9+99+999....)
Re arrange
=2/3((10-1)+(100-1) +(1000-1)-n))....)

=2/3(10+100+1000...-n)

=2/3 ( 10+10^2+10^3-n))

Sn = %282%2F3%29%28%2810%2810%5En-1%29%2F%2810-1%29%29+-n%29

Sn = %282%2F3%29%28%2810%2810%5En-1%29%2F%289%29%29+-n%29